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研究生:林銘杰
研究生(外文):Ming-Chieh Lin
論文名稱:開放式量子異質結構之準穩態研究
論文名稱(外文):Study on the Quasistationary States in Open Quantum Heterostructures
指導教授:褚德三褚德三引用關係
指導教授(外文):Der-San Chuu
學位類別:博士
校院名稱:國立交通大學
系所名稱:電子物理系
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:115
中文關鍵詞:開放式量子異質結構準穩態
外文關鍵詞:OpenQuantum HeterostructuresQuasistationary States
相關次數:
  • 被引用被引用:14
  • 點閱點閱:987
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
在本論文中,我們研究粒子在不同量子異質結構中的準穩態行為。首先,我們使用一個簡單的時域模型考慮電子在開放式耦合量子井中之準穩態的生命期。利用轉換矩陣法及特殊邊界給定可以得到一複變數色散方程並從而求得共振能階與生命期。
對於開放式量子線與量子點系統,我們引進了合超流幾何函數-複變引數之惠特克函數。利用此函數來表示電子在上述系統中的波函數,在異質介面邊界滿足特殊連續條件及假設等效質量近似條件下,我們可以得到一複數固有能量值色散方程式。所有的準穩態的共振能階與生命期可以被精確求得。求解此複變方程式需使用牛頓法在複數平面勘根求解。
此外,我們也使用微擾法研究激子在多層半導體量子點中的行為。我們發現等效介電常數法在許多情況下不適用。激子在開放式量子點的生命期近似的等於電子生命期。
最後,我們用自洽法研究場發射二極體的電性。場發射二極體的陰極表面電場只與材料表面功函數有關。
In this dissertation, we study the quasistationary states in open quantum heterostructures. The quasistationary states of an electron in an open coupled quantum well, an open quantum wire, and an open quantum dot are investigated. A simple time-dependent model is presented to investigate lifetimes of the quasistationary states in open coupled quantum wells. A complex-eigenenergy solver is presented to determine both the resonance positions ER and the corresponding lifetimes τ of the system for the latter two cases. In the eigen-solver, the wave functions are expressed in terms of the Whittaker functions with complex arguments, and the effective-mass Schrödinger equation is solved analytically. The quasistationary states in terms of the complex eigen-energies, ER-iħ/(2τ), are extracted numerically in the complex plane by Newton''s method. All the quasistationary states of the system can be determined. The system of an exciton in spherically N-layered semiconductor quantum dots is also investigated via the perturbation method. Finally, the quasistationary states of a relativistic field-emission-limited diode are investigated via a self-consistent approach.
Contents
1.Introduction 1
2.Quasistationary States in Open Coupled Quantum Wells 15
2.1 Introduction 16
2.2 Formulation 19
2.3 Results and Discussion 23
2.4 Conclusion 26
References 28
List of Figures 30
List of Tables 31
3. Quasistationary States of an Electron in Open Quantum
Wires 40
3.1 Introduction 41
3.2 Formulation 43
3.3 Results and Discussion 46
3.4 Conclusion 48
References 49
List of Figures 52
4. Quasistationary States of an Electron in Open Quantum
Dots 58
4.1 Introduction 59
4.2 Formulation 60
4.3 Results and Discussion 64
4.4 Conclusions 66
References 67
List of Figures 70
5. Excitonic States in Spherically Multilayered Quantum
Dots 76
5.1 Introduction 77
5.2 Theory 79
5.2.1 The Whittaker function approach 80
5.2.2 The Coulomb interaction 82
5.3 Results and Discussion 84
5.4 Conclusions 86
References 88
List of Tables and Figures 90
6. Quasistationary States of a Relativistic Field-Emission-
Limited Diode
6.1 Introduction 98
6.2 Formulation 99
6.3 Results and discussion 103
6.4 Conclusions 104
References 105
List of Figures 107
7. SUMMARY 112
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